Clustering discretization methods for generation of material performance databases in machine learning and design optimization

Mechanical science and engineering can use machine learning. However, data sets have remained relatively scarce; fortunately, known governing equations can supplement these data. This paper summarizes and generalizes three reduced order methods: self-consistent clustering analysis, virtual clustering analysis, and FEM-clustering analysis. These approaches have two-stage structures: unsupervised learning facilitates model complexity reduction and mechanistic equations provide predictions. These predictions define databases appropriate for training neural networks. The feed forward neural network solves forward problems, e.g., replacing constitutive laws or homogenization routines. The convolutional neural network solves inverse problems or is a classifier, e.g., extracting boundary conditions or determining if damage occurs. We will explain how these networks are applied, then provide a practical exercise: topology optimization of a structure (a) with non-linear elastic material behavior and (b) under a microstructural damage constraint. This results in microstructure-sensitive designs with computational effort only slightly more than for a conventional linear elastic analysis.